Big Understanding- Many real world situations can be modeled and predicted using mathematics.
Essential Question- What is the relationship between a table, a graph, and an equation?
2.3 Walking For Charity
In this problem, we will refer to Leanne, Gilberto, and Alana’s suggestions as [ledge plans.
A1. Make a table showing the amount of money a sponsor would owe under each pledge plan if a student walked distances between 0 and 10 miles.
A2. Graph the three pledge plans on the same coordinate axes. Use a different color for each plan.
A3. For each pledge plan, write an equation that can be used to calculate the amount of money a sponsor owes, given the total distance the student walks.
Leanne- y=x
Gilberto- y=2x
Alana- y=.5x+5
B. What effect does increasing the amount pledged per mile have on the table? The graph? The equation?
Table: The y-axis will go up with a larger number each time the x-axis goes up by 1.
Graph: The slope of the line will become steeper.
Equation: The co-efficient becomes larger.
C. If a student walks 8 miles in the walkathon, how much would a sponsor owe under each pledge plan? Explain how you got your answer.
Leanne- She would earn $8. 1 times 8=8
Gilberto- He would earn $16. 2 times 8=16
Alana- She would earn $9. .5 times 8 + 5=9
I used their equations to solve this problem.
D. For a sponsor to owe a student $10, how many miles would the student have to walk under each pledge plan? Explain how you got your answer.
Leanne- 10 miles. $10 divided by 1= 10 miles
Gilberto- 5 miles. $10 divided by 2= 5 miles
Alana- 10 miles. $10-5 divided by .5= 10 miles
I used the equations to solve these problems.
E. Alana suggested that each sponsor should make a $5 donation and then pledge 50 cents per mile. How is this fixed $5 donation represented in the table. In the graph? In the equation?
Table: When the number of miles is at zero the pledge money is $5.
Graph: The line enters the first quadrant at 5 on the y-axis.
Equation: It has +5 in the equation.
May 25, 2009
Block 7B
Big Understanding- Many real world situations can be modeled and predicted using mathematics.
Essential Question- What is the relationship between a table, a graph, and an equation?
2.3 Walking For Charity
In this problem, we will refer to Leanne, Gilberto, and Alana’s suggestions as [ledge plans.
A1. Make a table showing the amount of money a sponsor would owe under each pledge plan if a student walked distances between 0 and 10 miles.
Number of Miles Leanne Gilberto Alana
0 0 0 5
1 1 2 5.50
2 2 4 6
3 3 6 6.50
4 4 8 7
5 5 10 7.50
6 6 12 8
7 7 14 8.50
8 8 16 9
9 9 18 9.50
10 10 20 10
A2. Graph the three pledge plans on the same coordinate axes. Use a different color for each plan.
A3. For each pledge plan, write an equation that can be used to calculate the amount of money a sponsor owes, given the total distance the student walks.
Leanne- y=x
Gilberto- y=2x
Alana- y=.5x+5
B. What effect does increasing the amount pledged per mile have on the table? The graph? The equation?
Table: The y-axis will go up with a larger number each time the x-axis goes up by 1.
Graph: The slope of the line will become steeper.
Equation: The co-efficient becomes larger.
C. If a student walks 8 miles in the walkathon, how much would a sponsor owe under each pledge plan? Explain how you got your answer.
Leanne- She would earn $8. 1 times 8=8
Gilberto- He would earn $16. 2 times 8=16
Alana- She would earn $9. .5 times 8 + 5=9
I used their equations to solve this problem.
D. For a sponsor to owe a student $10, how many miles would the student have to walk under each pledge plan? Explain how you got your answer.
Leanne- 10 miles. $10 divided by 1= 10 miles
Gilberto- 5 miles. $10 divided by 2= 5 miles
Alana- 10 miles. $10-5 divided by .5= 10 miles
I used the equations to solve these problems.
E. Alana suggested that each sponsor should make a $5 donation and then pledge 50 cents per mile. How is this fixed $5 donation represented in the table. In the graph? In the equation?
Table: When the number of miles is at zero the pledge money is $5.
Graph: The line enters the first quadrant at 5 on the y-axis.
Equation: It has +5 in the equation.